 Solution

ID: past-exam-of-the-topics-in-applied-mathematics-course-of-the-university-of-oxford/2007/a/3/ii/a/solution

For

0 < a < η

f (a) = a (η^{2} - a^{2}) / (1 + a^{2}) > 0

. On the horizontal edge

b = 0

b^{'} = - f (a) < 0.

The vector field points downward into the proposed trapping region.

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